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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.13326 |
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| _version_ | 1866908837872664576 |
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| author | Eteve, Arnaud |
| author_facet | Eteve, Arnaud |
| contents | Let $\mathbf{G}$ be a connected reductive group over a finite field $\mathbb{F}_q$ of characteristic $p > 0$. In this paper, we study a category which we call Deligne--Lusztig category $\mathcal{O}$ and whose definition is similar to category $\mathcal{O}$. We use this to construct a collection of representations of $\mathbf{G}(\mathbb{F}_q)$ which we call the tilting representations. They form a generating collection of integral projective representations of $\mathbf{G}(\mathbb{F}_q)$. Finally we compute the character of these representations and relate their expression to previous calculations of Lusztig and we then use this to establish a conjecture of Dudas--Malle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tilting representations of finite groups of Lie type Eteve, Arnaud Representation Theory Let $\mathbf{G}$ be a connected reductive group over a finite field $\mathbb{F}_q$ of characteristic $p > 0$. In this paper, we study a category which we call Deligne--Lusztig category $\mathcal{O}$ and whose definition is similar to category $\mathcal{O}$. We use this to construct a collection of representations of $\mathbf{G}(\mathbb{F}_q)$ which we call the tilting representations. They form a generating collection of integral projective representations of $\mathbf{G}(\mathbb{F}_q)$. Finally we compute the character of these representations and relate their expression to previous calculations of Lusztig and we then use this to establish a conjecture of Dudas--Malle. |
| title | Tilting representations of finite groups of Lie type |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2412.13326 |